According to (REF ), the statistics of \({B}\)  are described by a Gaussian characteristic functional when \(\phi \)  is assumed to be Gaussian. Just as in previous works [1]}, [2]} when deriving a closure model for \(D_t{\mathcal {A}}\) , it is acknowledged that the statistics of \({B}\)  are not Gaussian in a real turbulent flow (nor are they Gaussian even when \({u}\)  is Gaussian [3]}). The motivation for this choice is simply that it is the only option when deriving a statistical field closure. It must be appreciated, however, that only with respect to the closure of \(\langle \nabla ^2{B}\rangle _{{\mathcal {A}},{\mathcal {B}}}\) , are the statistics of \({B}\)  approximated as being Gaussian; the model that follows from this choice nevertheless generates statistics for \({\mathcal {B}}\)  that are highly non-Gaussian (as will be shown later).
